Selecting faces on object from UV editor window
There's a button you can check to sync edit mode mesh selection with the uv editor:



Enable it, then select a UV face in UV editor and see it selected in View3D!

It doesn't work however for UV islands, and as you enable it, the selection in the View3D takes precedence over the UV selection. That's for sure something to be improved.

For Blender 2.8 

The button to toggle 'sync' is as shown below: